Two principle approaches to object detection have been proposed in the literature, searching for local maxima (Kron,1980;Yee,1991) and collecting consecutive pixels lying above a given threshold relative to the background noise, often called “thresh- olding”, (Jarvis & Tyson, 1981;Bertin & Arnouts,1996). While searching for local maxima is better in the presence of crowding since close-by objects are naturally de- tected as distinct objects, it is less robust at low signal-to-noise and with low surface brightness objects. A promising new possibility might be to use vision models to analyse isophote contour shapes in the image, searching for closed contours. Such an approach has not yet been investigated with respect to its usefulness in astronomy because it is still prohibitively expensive in terms of computing time.
We have therefore implemented thresholding, after convolution of the image with a Gaussian of FWHM equal to the seeing in the frame. The optimum convolution kernel for the detection of faint sources would be the image PSF (Irwin,1985), but for all practical purposes a Gaussian approximation is good enough, as comparisons have shown.
3.3.1 Background determination, thresholding, and object assembly Thresholding effectively means collecting pixels above a certain surface brightness and signal-to-noise ratio limit. Usually this limit is expressed in terms of the variance of the background noise present in the image. Of course one would like the statistical significance of such a detection to be independent of position in the image. Therefore an accurate local estimate of the background value and noise is needed.
The background and the rms noise in the background are estimated as a function of position in the convolved image by inspecting the histogram of pixel values in rect- angular regions of the image, usually 64×64 pixels in size. The pixels within each region are κ−σ filtered to minimise impact of bright objects and outliers, and the
histogram of their values is computed. The background and the rms value in each grid cell is estimated to be the mode and half of the width of the distribution at 1/e of the mode, respectively. The final background and rms values for each pixel are produced by bilinear interpolation between the grid cells. If necessary, background estimation can be improved by an iterative process of masking out pixels assigned to objects after thresholding and redetermining the background. This can be useful in the presence of bright stars, large galaxies, or moderate crowding.
Objects are detected by requiring that a minimum number N of consecutive pixels lie at least a certain thresholding factor t of the local rms above the local background. Consecutive here is defined as that at least one of the eight closest neighbours be above the threshold.
The values for N and t reflect a compromise between completeness at a given signal-to-noise – the magnitude limit – and the number of tolerable spurious detections per unit image area (Saha, 1995;Neuschaefer et al., 1995;Harris,1990), depending on the form and size of the PSF and the pixel scale in addition to the characteristics of the noise present. They have to be chosen carefully for any individual application of
the data.
3.3.2 Splitting of multiple components
Close objects can overlap at the detection isophote, in which case they will be wrongly assembled into a single object by the thresholding phase. Therefore each object is re-examined by thresholding it at a number of linearly spaced, increasingly higher isophotes up to a fixed fraction of its maximum flux.
If an object decomposes into several components at some isophote, the component containing the pixel of maximum flux of the original object retains this identity, the other components being considered as new objects. The new objects are added to the end of the catalogue (their “detection isophote” set to the current splitting isophote) and the original object is continued to be examined. To avoid splitting noise peaks in the wings of objects, the subcomponents are required to consist of a minimum number of consecutive pixels to be regarded as real.
3.3.3 Evaluation of shape parameters
After de-blending, structural parameters within the detection isophote for each object are computed, namely the intensity-weighted radius,
Re=∑
rI(r)
∑I(r) ,
the intensity-weighted first and second moments,
Cx = ∑∑xII((xx,,yy)), Cy = ∑∑yII((xx,,yy)), Ixx = ∑(x−Cx) 2I(x,y) ∑I(x,y) , Iyy = ∑(y−Cy)2I(x,y) ∑I(x,y) , Ixy = ∑(x −Cx)(y−Cy)I(x,y) ∑I(x,y) , the elongation, E= p (Iyy−Ixx)2+ (2Ixy)2 Ixx+Iyy ,
and the full width at half maximum,
FW HM=2pln 2(Ixx+Iyy),
where I(x,y)denotes the background subtracted intensity at pixel (x,y), and r2= (x−Cx)2+ (y−Cy)2, the Euclidean distance from the object’s centre. The sums are to
be taken over all pixels within the detection isophote.
For computing elliptical aperture shapes in the case where adaptive-size (“Kron- like”) apertures are to be used for photometry, the major and minor axes A and B, as well as the position angleθ, are computed based on the second moments:
A2 = Ixx+Iyy 2 + s Ixx−Iyy 2 2 +Ixy2, B2 = Ixx+Iyy 2 − s Ixx−Iyy 2 2 +Ixy2, and, tan 2θ = 2 Ixy Ixx−Iyy .
The background flux, the flux at the detection isophote and the total flux within the detection isophote as well as the central and mean surface brightness are also com- puted. These quantities comprise the final output of the object detection and assembly phase.